{
  "id": "1009.0872",
  "version": "v3",
  "published": "2010-09-04T21:00:58.000Z",
  "updated": "2011-12-03T19:06:35.000Z",
  "title": "Primitive Divisors of Certain Elliptic Divisibility Sequences",
  "authors": [
    "Paul Voutier",
    "Minoru Yabuta"
  ],
  "comment": "version accepted for publication. Difference of heights result moved to http://arxiv.org/abs/1104.4645 and improved. Proof simplified to remove need for special cases when n>20",
  "journal": "Acta Arith. 151 (2012), 165-190",
  "doi": "10.4064/aa151-2-2",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $P$ be a non-torsion point on the elliptic curve $E_{a}: y^{2}=x^{3}+ax$. We show that if $a$ is fourth-power-free and either $n>2$ is even or $n>1$ is odd with $x(P)<0$ or $x(P)$ a perfect square, then the $n$-th element of the elliptic divisibility sequence generated by $P$ always has a primitive divisor.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-12-03T19:06:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11A41"
    ],
    "keywords": [
      "primitive divisor",
      "perfect square",
      "th element",
      "elliptic curve",
      "elliptic divisibility sequence"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.0872V"
    }
  }
}